Elements of geometry and trigonometry. Revised and adapted to the course of mathematical instruction in the United States (1856)
Legendre, A. M. (Adrien Marie), 1752-1833, Davies, Charles, 1798-1876 · New York : A.S. Barnes · leaf 225
scribed circle: then, if this semi-polygon be re-volved about GF^ the solid generated will have for itsmeasure, iarea OIxGF. For, since the polygon is regular,the triangles, OF A, OAB, OBC, kc, areisosceles and equal; then, all the per-pendiculars let fall from 0 on theirbases, will be equal to Oi,… … BOOK YIII. 221 hence, the entire solid generated by the semi-poljgon ismeasured by f ^X 01\fM+MN+N0^ OQ+QR+BG) : that is, by ^rrXOI^GF. But, X X Ol=area 01 (b. v., p. 16): hence. solidity = I area OIxGF. TEOPOSITION XIV. THEOREM. The solidity of a sphere is equal to its surface multiplied hy athird…
Geometry · Trigonometry
Internet Archive · California Digital Library · Public Domain Mark 1.0. Free to use for anything.
